After thinking about the different uses of those prepositions, I think it comes down to which verb is used before them. I can’t think of another use of “at page” except after a verb like look to direct someone to ”Look at page 32”, for example. “Look on page 32” could also be used there though. The most common use in “on page” I can think of is describing what information “is on” a page. So a form of the verb to be would work there. For example, “The answer was on page 32.” various particles can fit in between there though such as “The answer was found on page 32.” The version “to page” would most often come after a verb like ”turn”. For example, “Turn to page 32 please.” If you can give examples of specific difficulties you have had, we might be able to help more.

Hello. I did a Google search on "at page or on page grammar" as I was not familiar with "at page". That lead me to this question '“In page” or “on page”, which preposition?' (https://ell.stackexchange.com/questions/107305/in-page-or-on-page-which-preposition/142190), which had a good answer to "on page" but the answer also mentioned "From Longman Dictionary of Contemporary English", which has a rather complete description of page: https://www.ldoceonline.com/dictionary/page